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In the setting of the Binomial Distribution, I am trying to figure out how to plot the probability of obtaining $k \ge 31$ for fixed $n$, for success probabilities $p$ between $0$ and $1$.

Why does the code below not work?

DiscretePlot[Table[CDF[BinomialDistribution[50, p], k], {k, {31}}] // Evaluate, {p, 1}, ExtentSize -> Left]
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2 Answers 2

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Plot[SurvivalFunction[BinomialDistribution[50, p], 30], {p, 0, 1}]

Mathematica graphics

Note: As noted by @user120911, this function simplifies to BetaRegularized[p, 1 + m, -m + n]

FullSimplify[SurvivalFunction[BinomialDistribution[n, p], m],
 {m, n} ∈ Integers && n > m >= 0]

 BetaRegularized[p, 1 + m, -m + n]

So

Plot[BetaRegularized[p, 1 + 30, -30 + 50], {p, 0, 1}]

gives the same picture.

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  • $\begingroup$ You need 30, not 31... $\endgroup$
    – ciao
    Commented Jun 6, 2017 at 23:16
  • $\begingroup$ @kglr, it turns out your solution simplifies nicely to the Regularized Beta Function. $\endgroup$
    – user120911
    Commented Jun 19, 2017 at 9:32
  • $\begingroup$ @user120911, good observation. I added your comment to the post. $\endgroup$
    – kglr
    Commented Jun 19, 2017 at 23:31
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Plot[Probability[k >= 31, 
  k \[Distributed] BinomialDistribution[50, p]], 
  {p, 0, 1}]

enter image description here

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